Question

Solve the given inequality: $4x+3<5x+7$ .

Answer 1

Hint: In this question, we have been given an inequality, which we can solve by subtracting (4x+7) from both sides to find an simplified inequality in terms of x. Remember that the operations like addition of terms and subtraction of terms follow the same set of rules which are used in case of equation, while the rules for operations like multiplication and division are quite different for inequalities.

Complete step-by-step answer:
The given inequality is
$4x+3<5x+7$
We know that an inequality remains valid if we add or subtract the same number both in the Left Hand Side (LHS) and Right Hand Side (RHS). Therefore, we should subtract a number on both sides such that only x remains on the RHS. So, we will subtract (4x+7) from both sides of the inequality.
$4x+3-\left( 4x+7 \right)<5x+7-\left( 4x+7 \right)$
$\Rightarrow 4x+3-4x-7<5x+7-4x-7$
$\Rightarrow -4 < x $
So, the inequality is valid for all the values of x that are greater than -4. This can be mathematically represented as $x\in \left( -4,\infty \right)$ .

Note: Whenever dealing with an inequality be very careful while we multiply, square or perform other operations, as there are cases where the sign of inequality changes. For example: x>y implies $-y>-x$ , i.e. , when both sides of a inequality are multiplied by a negative number, the sign of inequality changes. Also, be careful about the calculation and the signs while opening the brackets. The general mistake that a student can make is \[-\left( 4x+7 \right)=-4x+7\] .